The purpose of this study is to evaluate the effectiveness of ProstAtak® immunotherapy in patients undergoing active surveillance for localized prostate cancer. ProstAtak® involves the use of aglatimagene besadenovec (AdV-tk) to kill tumor cells and stimulate a cancer vaccine effect. Killing tumor cells in an immune stimulatory environment induces the body's immune system to detect and destroy cancer cells. ProstAtak® has been well tolerated in previous trials in patients with prostate cancer and other tumor types. Biochemical, pathologic and immune responses have been demonstrated in newly diagnosed and recurrent prostate cancer. The hypothesis is that ProstAtak can lead to improvement in the clinical outcome for patients with prostate cancer. Participants will be randomized to the ProstAtak® or control arm at a 2:1 ratio. Both arms receive standard of care active surveillance evaluations.